「運動論方程式,流体力学とその周辺」(第3回)

下記のとおり日本航空宇宙学会関西支部分科会による講演会を開催しますのでご案内いたします.

http://www.mfd.kuaero.kyoto-u.ac.jp/?cat=16


日時: 平成30年8月24日(金) 15:00-17:00
場所: 京都大学 桂キャンパスCクラスタ総合研究棟III(C3棟) 3階 b3n03室(航空宇宙工学専攻会議室)

題目1:
Entropy methods and cross-diffusion systems: derivation and entropy
structure
講演者1:
Prof. Ansgar Jüngel
(Institute for Analysis and Scientific Computing, Vienna University of
Technology, Austria)
要旨1:
Nature is dominated by systems composed of many individuals, belonging to
various species, with a collective behavior. Instead of calculating the
trajectories of all individuals, it is computationally much simpler to
describe the dynamics of the individuals on a macroscopic level by averaged
quantities such as population densities. This leads to systems of highly
nonlinear partial differential equations with cross diffusion, which may
reveal surprising effects such as uphill diffusion and diffusion-induced
instabilities. In this talk, we detail some approaches on the derivation of
cross-diffusion equations from kinetic, fluiddynamical, and stochastic
models. Relations to thermodynamic principles and the results of Kawashima
and Shizuta are detailed. The entropy structure can also be found in
nonstandard applications like van-der-Waals fluids, population dynamics,
and exotic financial derivatives. It allows for a mathematical existence
theory and stable numerical approximations with guaranteed lower and upper
bounds.

題目2:
Linear Boltzmann equation and fractional diffusion
講演者2:
Prof. François Golse
(Centre de mathématiques Laurent Schwartz, Ecole Polytechnique, France)
要旨2:
Consider the linear Boltzmann equation of radiative transfer in a
half-space, with constant scattering coefficient σ. Assume that, on the
boundary of the half-space, the radiation intensity satisfies the Lambert
(i.e. diffuse) reflection law with albedo coefficient α. Moreover, assume
that there is a tem- perature gradient on the boundary of the half-space,
which radiates energy in the half-space according to the Stefan-Boltzmann
law. In the asymptotic regime where σ → +∞ and 1 – α ~ C/σ, we prove that
the radiation pressure exerted on the boundary of the half-space is
governed by a fractional diffusion equation. This result provides an
example of fractional diffusion asymptotic limit of a kinetic model which
is based on the harmonic extension definition of √-Δ. This fractional
diffusion limit therefore differs from most of other such limits for
kinetic models reported in the literature, which are based on specific
properties of the equilibrium distributions (“heavy tails”) or of the
scattering coefficient as in [U. Frisch-H. Frisch: Mon. Not. R. Astr. Not.
181 (1977), 273-280].

以上


問い合せ先:
京都大学 航空宇宙工学専攻
初鳥 匡成
〒615-8540 京都市西京区京都大学桂4 桂キャンパスC3棟c3S05室
TEL: 075-383-3781
E-mail: hattori.masanari.4r@kyoto-u.ac.jp